Method and corresponding arrangement for DC offset compensation using channel estimation

ABSTRACT

A method of determining a DC offset in a communications signal received via a communications channel, the communications signal comprising a sequence of training symbols. The method comprises providing a channel estimate of the communications channel based on said sequence of training symbols; determining, based on the channel estimate, an estimate of a noise contribution introduced by the communications channel; and determining an estimate of the DC offset from the determined estimate of the noise contribution.

This patent application claims the benefit of priority from U.S.Provisional Patent Application Ser. No. 60/429,618 filed on Nov. 26,2002. This application incorporates by reference the entire disclosureof U.S. Provisional Patent Application Ser. No. 60/429,618.

The present invention relates to the determination of a DC offset in acommunications signal received via a communications channel. Inparticular, the invention relates to the determination of a DC offset ina communications signal received via a communications channel, thecommunications signal comprising a sequence of training symbols.

In a digital communications system, such as a system according to TDMA1,GSM, EDGE, or the like, data is encoded into symbols, packed into burstsand modulated prior to transmission via a physical transmission channel.At the receiver, the demodulation is performed and includes an equalizerwhich compensates for channel distortions, e.g. due to Inter-symbolinterference (ISI).

For many communications system, in particular mobile telecommunicationssystems, the design of the receiver architectures is governed byrequirements to be cost effective, small sized, and having low powerconsumption. Unfortunately, many such receiver architectures suffer fromDC-offsets introduced in the communications system, in particularreceivers, such as homodyne receivers, that directly convert the radiofrequency signal into a baseband signal.

A DC offset may be introduced by a number of different sources, e.g. dueto a local oscillator signal leaking to and reflecting off the antennaand being down converted to DC, due to a large near-channel interfererwhich is leaking into the local oscillator, due to a component mismatchin the signal path, or due to other reasons. Even though some of theabove sources for DC offsets can be reduced to some extend by a carefulfront-end design, in many communications system a DC offset is stillpresent at the baseband processing and may cause significant receiverperformance degradation. Hence it is desirable to provide accurateestimates of DC offsets in order to allow for their compensation.

International patent application WO 01/03396 discloses a method ofsimultaneously estimating the transmission channel and the DC offset.According to this prior art method, the DC offset is treated as an extratap in the multi-tap channel estimation.

It is a problem of the above prior art method that the simultaneouschannel and DC offset estimation involves a significant computationalcomplexity. It is a further problem that due to the extra tap anadditional parameter is to be estimated, thereby compromising thequality of the channel estimation.

The above and other problems are solved by a method of determining a DCoffset in a communications signal received via a communications channel,the communications signal comprising a sequence of training symbols; themethod comprising

providing a channel estimate of the communications channel based on saidsequence of training symbols;

determining, based on the channel estimate, an estimate of a noisecontribution introduced by the communications channel; and

determining an estimate of the DC offset from the determined estimate ofthe noise contribution.

According to the invention, it has been realized that an estimation ofthe DC offset based on noise samples obtained from an initial channelestimate provides a considerably improved performance.

It has further been realized that the method according to the inventionreduces the complexity of the processing.

The term DC-offset comprises low frequency distortion of the receivedsignal. The term “low frequency distortion” in this context comprisesdistortions having a rate of change which, if any, is slow compared tothe dynamics of the radio channel and the rate of the transmittedinformation (e. g., the low frequency distortion is relatively constantover the span of two transmitted symbols).

In a preferred embodiment of the invention, the step of determining theestimate of the noise contribution comprises determining the estimate ofthe noise contribution from a difference between a number of receivedtraining symbols and corresponding expected training symbols based onthe determined channel estimate. Hence, an efficient noise estimate isprovided.

In another preferred embodiment, the step of providing the channelestimate comprises treating a potential DC offset as an uncharacterizedinterference contribution, i.e. without considering the DC offset,thereby allowing a subsequent estimate of the DC offset based on theestimated noise.

In yet another preferred embodiment, the step of determining an estimateof the DC offset from the determined estimate of the noise contributioncomprises calculating an inner product of a rotation trend vector and anestimated noise vector representing the determined estimate of the noisecontribution. Hence, a computationally efficient estimation is providedthat only requires n-m complex multiply and accumulate (MAC) operationswhere n is the number of training symbols and m is the size of theequalizer window and, thus related to the delay spread of the receivedradio signal. This is a significant reduction in complexity compared tothe complexity of the joint channel-DC estimation of the above-mentionedprior art approach.

In another preferred embodiment, the step of determining the channelestimate comprises simultaneously determining a desired synchronizationposition of the sequence of training symbols with respect to a receivedsignal burst of the communications signal and a desired size of anequalizer window of a channel estimation-based equalizer. It has furtherbeen realized by the inventor that a simultaneous estimation of thesynchronization position and equalizer window size of the receiver maybe performed which is robust against any DC offsets and, at the sametime, yields an initial channel estimate which may advantageously beused in the DC offset determination according to the invention. Hence,by determining the synchronization position and equalizer span prior tothe DC offset estimation, a channel estimate is provided by thesynchronization and equalizer span adaptation without additionalcomputational cost, thereby further decreasing the complexity of the DCoffset compensation.

In a further preferred embodiment, the method further comprisesdetermining a number of channel estimates of the transmission channel asa function of the synchronization position and a size of the equalizerwindow; determining the desired synchronization position and the desiredsize of the equalizer window by calculating an error measure based onthe received signal burst and the determined estimates for a number ofselected values of the synchronization position and of the size of theequalizer window.

It has been realized that the above method of burst synchronization andequalizer span sizing yields a burst synchronization which is robustagainst residual DC components after burst averaging.

In a yet further preferred embodiment, the step of determining thedesired synchronization position and the desired size of the equalizerwindow by calculating an error measure based on the received signalburst and the determined estimates for a number of selected values ofthe synchronization position and of the size of the equalizer windowcomprises selecting the values of the size of the equalizer windowbetween predetermined upper and lower bounds; and the method furthercomprises determining the upper and lower bounds based on at least adesired size of the equalizer window as determined for a previouslyreceived signal burst. Consequently, an adaptive aperture for the spanadaptation is provided.

It has been realized that the physical channel in a digitalcommunications system does not change instantly with respect to thedelay spread in contrast to, for example, the strength and phase of asignal which may experience rapid fluctuations. Based on thisunderstanding, the aperture of the equalizer span can be made adaptive,i.e. the aperture for a current span optimization may be determinedbased on the determined equalizer spans for one or more previous bursts.

In another preferred embodiment, the method further comprises averagingthe received communications signal over a received signal burst, therebyproviding a signal as an input to the initial channel estimation, wherea considerable portion of the DC offset is removed. Consequently, thequality of the subsequent processing is further improved.

Preferably, the communications signal comprises a signal in accordancewith the GSM specifications or in accordance with the EDGEspecifications. EDGE (Enhanced Data rates for Global Evolution) is aninterface mode which has recently been developed for GSM Networks.EDGE's principal features include new modulation and coding schemeswhich increase data capacity and speed in the air interface. EDGE isfully based on GSM and uses the same TDMA (Time Division MultipleAccess) frame structure as GSM, such that it allows GSM operators to useexisting GSM radio bands to offer wireless multimedia-based services andapplications.

The present invention can be implemented in different ways including themethod described above and in the following, an arrangement, and furthermethods and product means, each yielding one or more of the benefits andadvantages described in connection with the first-mentioned method, andeach having one or more preferred embodiments corresponding to thepreferred embodiments described in connection with the first-mentionedmethod and disclosed in the dependant claims.

It is noted that the features of the method described above and in thefollowing may be implemented in software and carried out in a dataprocessing system or other processing means caused by the execution ofcomputer-executable instructions. The instructions may be program codemeans loaded in a memory, such as a RAM, from a storage medium or fromanother computer via a computer network. Alternatively, the describedfeatures may be implemented by hardwired circuitry instead of softwareor in combination with software.

The invention further relates to a method of compensating a DC offset ina communications signal received via a communications channel, thecommunications signal comprising a sequence of training symbols; themethod comprising

determining a DC offset in the communications signal according to themethod described above and in the following; and

manipulating the communications signal to compensate for the determinedDC offset.

In a preferred embodiment, the method further comprises

determining a channel estimate of the communications channel based onthe manipulated communications signal;

filtering the manipulated communications signal in an equalizer based onthe determined channel estimate.

The invention further relates to and arrangement for determining a DCoffset in a communications signal received via a communications channel,the communications signal comprising a sequence of training symbols; thearrangement comprising processing means adapted to provide a channelestimate of the communications channel based on said sequence oftraining symbols;

processing means adapted to determine, based on the channel estimate, anestimate of a noise contribution introduced by the communicationschannel; and

processing means adapted to determine an estimate of the DC offset fromthe determined estimate of the noise contribution.

The term processing means comprises any suitable general- orspecial-purpose programmable microprocessor, Digital Signal Processor(DSP), Application Specific Integrated Circuit (ASIC), ProgrammableLogic Array (PLA), Field Programmable Gate Array (FPGA), special purposeelectronic circuit, etc., or a combination thereof.

The invention further relates to a receiver for receiving acommunications signal via a transmission channel, the receivercomprising means for receiving a communications signal and anarrangement for determining a DC offset in the communications signal asdescribed above and in the following.

The means for receiving a communications signal may include any deviceor circuitry suitable for receiving signal bursts of a communicationsscheme used in a digital communications system. Examples of such areceiver include a radio receiver, e.g. a radio receiver in a digitalcommunications system according to GSM, EDGE, or the like.

The receiver may be part of an electronic equipment where the termelectronic equipment includes all stationary and portable radiocommunication equipment and other handheld or portable devices. The termportable radio communication equipment includes all equipment such asmobile telephones, pagers, communicators, i.e. electronic organisers,smart phones, personal digital assistants (PDAs), handheld computers, orthe like.

The above and further aspects of the invention will be described in moredetail in connection with a preferred embodiment and with reference tothe drawing in which

FIG. 1 schematically illustrates a general model of a communicationssystem;

FIG. 2 illustrates the structure of a TDMA frame used in a digitalcommunications system according to the GSM/EDGE standard;

FIG. 3 shows a schematic block diagram of a receiver according to anembodiment of the invention;

FIG. 4 shows a flow diagram of a DC offset determination according to anembodiment of the invention;

FIG. 5 shows a schematic block diagram of the joint synchronization andequalizer span adaptation; and

FIG. 6 shows a flow diagram of burst synchronization and span adaptationaccording to a preferred embodiment of the invention.

FIG. 1 schematically illustrates a general model of a communicationssystem. The communications system comprises a transmitter 101 and areceiver 102 communicating via a communications channel 103. Forexample, in an actual implementation the transmitter may be a mobileterminal and the receiver a base station of a cellular radio frequency(RF) communications system or vice versa. The mobile terminal and thebase station communicate with each other via communications signalstransmitted over an air interface. For the purposes of the followingdescription, the transmitter 101 is considered to comprise a modulator105 which applies the necessary modulation to the signal so that it canbe transmitted over the communications channel. The receiver comprises ademodulator 106 implementing a demodulation process corresponding to themodulation process implemented by the modulator 105, thereby allowing torecover the originally transmitted information from the received signal.

For the purpose of the present description, the modulation anddemodulation processes mentioned above can be thought of as introducinga DC offset and a phase shift. The magnitude of the DC offset is unknownand causes problems in subsequent DSP processing steps on the receivedsignal, if it is not removed. The phase shift depends on the modulationmethod used and is known. Each signal symbol is modulated prior totransmission and experiences a phase shift depending on the modulationtechnique used. This phase shift is also known as rotation and may berepresented as a rotation by an angle α, i.e. by a factor exp(j α) wherej is the complex indicator.

For example, in EDGE the selected modulation is 3π/8-8PSK. In the basic8PSK constellation there are 8 equidistant points on the unit circle.This means that the transmitted symbols x_(k) can assume eight possiblevalues, x_(k)=exp(j·i·π/4) where i=0 , . . . , 7 depending on the symbolvalue, i.e. the bit sequence to be communicated. Now for 3π/8-8PSK, the3·π/8 shift means that the transmitted symbols are multiplied by a 3π/8rotating value yielding x′_(k)=x_(k)·exp(j·k·3·π/8), where k is thesymbol index.

At the receiver, the received symbols are de-rotated accordingly by anangle −α. For example, in EDGE, the symbols are de-rotated byexp(−j·k·3·π/8) to get the original 8PSK constellation to be equalised.However, this de-rotation will also make any DC offset which may existin the signal rotate by exp(−j·k·3·π/8), thereby causing an additiverotating trend in the received signal.

FIG. 2 schematically illustrates the structure of a TDMA frame 200 usedin a mobile telecommunications system according to the GSM standard. Fora TDMA system according to the GSM standard, mobile stations transmitbursts as modulated signals on respective carrier frequencies accordingto channels allocated to respective calls by a base station controller.One frequency channel may support up to eight calls, each call beingassociated with a respective burst, where each call is allocated a timeslot in a TDMA frame in which to send the burst. In FIG. 2, frame 200has a duration of 4.615 ms and accommodates 8 information channels (timeslots) 201, designated 0-7 in FIG. 2. Each of the 8 time slots has aduration of 0.577 ms and contains a 148-bit signal portion and a guardportion (not shown) which functions to maintain separation betweensignals in adjacent time slots. The 148-bit signal portion is generallyreferred to as a normal burst and comprises a first 3-bit tail bitsection 202, a first 57-bit coded data section 203, a first 1-bithousekeeping bit section 204, a 26-bit trailing sequence section 205, asecond 1-bit housekeeping bit section 206, a second 57-bit coded datasection 207 and a second 3-bit tail bit section 208. The 26-bitscomprising the training sequence section 205 in a GSM digitalcommunications system, is typically viewed as being divided into acentrally located portion 210 of 16-bits (sometimes referred to as themid-amble portion), and side portions 209 and 211 of 5-bits each.Alternatively, in a GSM/EDGE digital communications system, the 26-bittraining sequence 205 can be also viewed as including a 16-bit whitesequence and a 10-bit cyclic prefix. Further details of a TDMA systemaccording to the GSM standard are not described herein because they areknown to a person skilled in the art.

It is noted that, alternatively, other burst structures providing asuitable sequence of training symbols may be used.

In digital communications systems, inter-symbol interference can occuras a result of time dispersion in the transmission channel over which asignal is transmitted. In GSM/EDGE systems, the usual way to compensatefor ISI is to provide a channel estimation based equalizer in thereceiver. A correct burst synchronization is essential to theperformance of the equalizer.

FIG. 3 shows a schematic block diagram of a receiver according to anembodiment of the invention. The receiver 102 comprises an averagingblock 301, a de-rotation block 302, a synchronization and spanadaptation block 303, a trend estimation block 304, a DC correctionblock 305, a channel estimator 306, and an equalizer 307.

The averaging block 301 receives the received signal and performs anaveraging of the received signal over a burst, and removes any DC offsetidentified by the averaging. However, typically this simple approachdoes not remove the entire DC but leaves a residual DC offset.

The de-rotating block 302 de-rotates the received symbols by apredetermined angle according to the modulation scheme used and as wasdescribed in connection with FIG. 1.

The synchronization block 303 identifies the portion of the receivedsignal that corresponds to the training sequence: As mentioned above,the signals are transmitted in bursts. At the receiver, the shape of areceived burst is the result of the transmitted burst and thedistortions introduced by the transmission channel, such as noise,multi-path propagation, etc. The task of burst synchronization involvesthe task of determining a suitable position p of the training sequencewithin the received burst.

In one embodiment, this may be achieved by setting the equalizer windowsize m to a predetermined value and by performing burst synchronizationusing a Least-Squares Error (LSE) method. This approach requires aninitial channel estimation ĥ_(p) for each possible synchronizationposition p. The desired synchronization position is then determined byminimizing a square error according to

${p = {\arg\;{\min( {\sum\limits_{k}{{{r(k)} - {{\hat{r}}_{p}(k)}}}^{2}} )}}},$where

${{\hat{r}}_{p}(k)} = {\sum\limits_{i = 0}^{m - 1}{{h_{p}( {m - 1 - i} )} \cdot {t( {k + 1} )}}}$is an estimate of the received symbol based on the initial channelestimate ĥ_(p).

In a preferred embodiment of the invention, the burst synchronization iscombined with an optimization of the window size m of the equalizer, aswill be described in greater detail below.

The trend estimation block 304 identifies any residual rotation trendcaused by a residual DC offset not eliminated by the averaging block301. The trend estimation block 304 receives the initial channelestimate from the synchronization block 303 and determines the residualrotation trend, as will be described in greater detail below.

The DC offset corrector 305 receives the estimated rotation trend fromthe trend estimation block 304 and corrects the baseband signal for thedetected offset prior to feeding the signal into the channel estimator306 and the equalizer 307.

The equalizer 307, e.g. a Viterbi equalizer, compensates for the channeleffects and demodulates the relevant portions of the received basebandsignal that corresponds to the received data. The transmissioncharacteristics of the transmission channel frequently change due to avariety of factors, including the motion of the mobile terminals, thefluctuation of multi-path (time dispersive) propagation channels andvariant interferences introducing noise. As is well-known to thoseskilled in the art, the multipath channel and the noise component canadversely affect the quality of the received signal, e.g., causeintersymbol interference; and this necessitates that the received signalbe corrected, typically by means of channel estimation-based equalizer.

Specifically, the equalizer 307 attempts to correct the received signalutilizing an estimate of the transmission channel. The equalizer 307generates data representing an estimate of the actual transmittedsymbols for further processing by the receiver.

The receiver further comprises a channel estimator 306 which computes anumber of filter taps h_(i), i=1, . . . , m corresponding to theselected window size m of the equalizer. The channel estimate generatedby the channel estimator 306 is fed into the equalizer 307.

FIG. 4 shows a flow diagram of a DC offset determination according to anembodiment of the invention.

In order to describe the trend estimation block in greater detail, weconsider a signal burst comprising a training sequencet=[t₀t₁ . . . t_(n-1)]^(T)of length n that is sent from the transmitter 101 to the receiver 102.In the receiver 102, the signal is fed into the averaging block 301, thede-rotating block 302 and the synchronization block 303 as described inconnection with FIG. 3. The resulting de-rotated signal after burstsynchronization can be modeled as a vector in baseband according tor=[r ₀ r ₁ . . . r _(n-m)]^(T) =Φh+ηq+v.Hence, r comprises a contribution from the transmission channel which isa function of the channel vectorh=[h₀h₁ . . . h_(m−1)]^(T)and a regression matrix

$\Phi = {\begin{bmatrix}t_{m - 1} & t_{m - 2} & \cdots & t_{1} & t_{0} \\t_{m} & t_{m - 1} & \cdots & t_{2} & t_{1} \\\vdots & \vdots & ⋰ & \vdots & \vdots \\t_{n - 2} & t_{n - 3} & \cdots & t_{n - m} & t_{n - m - 1} \\t_{n - 1} & t_{n - 2} & \cdots & t_{n - m + 1} & t_{n - m}\end{bmatrix}.}$

Here, m is the channel span corresponding to the delay spread of thepropagation channel in terms of symbols. The above expression for rfurther comprises a rotating trend contribution which is caused by a DCoff-set in the received signal which is transformed into a rotatingtrend by the de-roation of block 302. The rotating trend is modeled as arotation trend vectorq=[1e ^(−jα) e ^(−j2α) . . . e ^(−j(n-m−1)α)]multiplied by the amplitude η of the residual DC offset. Here, α denotesthe rotation increment which depends on the modulation method used asdescribed above. For example, in GSM α=π/2 while in EDGE α=3π/8.

Finally, the above expression for r comprises a noise vectorv=[v₀v₁ . . . v_(n-m)]^(T).

According to the invention, in order to compensate for the DC offset,initially, in step 401 an initial LSE channel estimateĥ=(Φ* Φ)⁻¹ Φ* r

is provided without considering the residual DC offset, i.e. by treatingthe DC offset as an uncharacteristic interference contribution. Here ( .. . )* denotes complex conjugate transposition. In the case of realtraining sequences, as in GSM and EDGE, this reduces to plaintransposition.

In step 402, the corresponding initial estimation of the noise samplesis calculated according to{circumflex over (v)}=r−Φĥ.

In a preferred embodiment of the invention, step 401 comprises a jointoptimization of the synchronization position and the equalizer spanadaptation as described below. The resulting synchronization is robustagainst a residual DC offset, i.e. it is not critically influenced bythe presence of any DC offset.

For such a channel estimate which is robust against residual DC, thenoise samples can be considered as a function of the rotating trend,according to{circumflex over (v)}=r−Φĥ=ηq+v′,where v′ represents errors due to inaccuracies in the estimation.

Hence, from the calculated noise samples, in step 403 a Least Square(LS) estimate of the rotation trend is derived according to

$\eta = {{( {q*q} )^{- 1}\; q*\hat{v}} = {\frac{q*\hat{v}}{n - m + 1}.}}$

Here, the second identity is due to the fact that the rotation vector isof unit length, thereby yielding a simple number as the inverse of theinner product of the rotation vector. Hence, in step 403 the magnitude ηof the DC offset is calculated as a scaled inner product of the rotationtrend vector q and the initial estimate {circumflex over (v)} of thenoise samples.

Finally, the resulting complex number η indicative of the rotating trenddue to the DC offset, is used in the final step 404 to correct for theresidual DC offset, i.e. by subtracting the term ηq from the receivedsignal and feeding the resulting DC corrected signalr′=r−ηqinto the final channel estimator, i.e. the channel estimator 306 of FIG.3.

It is noted that the above estimation of the DC offset only requires n-mcomplex MAC operations which is a significant reduction in complexitycompared to the complexity of the joint channel-DC estimation of theabove-mentioned prior art approach.

FIG. 5 shows a schematic block diagram of the joint synchronization andequalizer span adaptation.

As mentioned above, in a preferred embodiment of the invention, thereceiver comprises a joint synchronization and span adaptation module303 which performs a joint determination of a synchronization position pand a size m of the equalizer window.

The joint synchronization and span adaptation module 303 comprises anoptimization module 501 for the joint optimization of the equalizer spanand the synchronization position within a predetermined interval ofwindow sizes. Accordingly, the synchronization and span adaptationmodule 303 further comprises an aperture module 502 which determines anupper and a lower bound m_(u) and m_(l), respectively, of the windowsize to be used by the optimization module for the synchronization ofthe subsequent burst. The aperture module 502 receives the determinedwindow size m for a current burst from the optimization module 501 andfeeds resulting bounds for the next burst back to the optimisationmodule 501.

FIG. 6 shows a flow diagram of burst synchronization and span adaptationaccording to a preferred embodiment of the invention.

The embodiment of FIG. 6 provides an efficient channel estimation methodby recognizing and utilizing two previously unexploited properties ofGSM/EDGE training sequences which arise from the cyclic prefix structureof the training sequences. In particular, this embodiment recognizesthat the 26-symbol GSM/EDGE training sequences are, within certainranges, both shift invariant and order invariant. The property of beingshift invariant enables a channel estimation to be carried out withdelayed (shifted) training sequence segments. This, in turn, permits: I.The ISI corrupted leading training sequence symbols to be avoided asmuch as possible in long dispersive channels; and II. The leading tapsof a channel to be estimated using the same training sequence segments,regardless of the size of the equalizer window. The property of beingorder invariant permits channels with different time dispersion, from1-8 symbols (as complex polynomials of 1-8th order) to be estimatedwithout matrix inversion if any consecutive 16-symbol segment of thetraining sequence is used.

In particular, upon receipt of a signal burst r(k) in step 601, a LeastSquare Error algorithm is performed to determine the equalizer windowspan m and the synchronization position p as illustrated by the loopcomprising steps 602-605.

According to this embodiment, the equalizer window span m and thesynchronization position p are determined as

$\begin{matrix}{{( {p,m} )_{opt} = {{\underset{p,m}{\arg\;\min}( {ɛ^{2}( {p,m} )} )} = {\underset{p,m}{\arg\;\min}( {\alpha^{m} \cdot {e^{2}( {p,m} )}} )}}},\begin{matrix}{{p = 0},1,\ldots\mspace{14mu},{w - 1}} \\{{m = m_{l}},\ldots\mspace{14mu},m_{u}}\end{matrix}} & (1)\end{matrix}$where ε(p,m)=α^(m/2)·e(p,m) is a generalized error measure derived fromthe error function

${e( {p,m} )} = {\sqrt{\sum\limits_{k}{{{r(k)} - {{\hat{r}}_{p,m}(k)}}}^{2}}.}$

Here

${{\hat{r}}_{p,m}(k)} = {\sum\limits_{i = 0}^{m - 1}{{{\hat{h}}_{p,m}( {m - 1 - i} )} \cdot {t( {k + 1} )}}}$is an estimate of the received signal expressed as a function of m andp, i.e. e(p,m) is a measure of the noise power introduced by theestimated transmission channel ĥ_(p,m) on the training sequence t. It isnoted that, in a practical implementation, the square root in the abovedefinition of the error function e(p,m) may be omitted, i.e. the squareof the error may be used instead.

If the noise power is used directly as an error function foroptimization, the channel window size m tends to be larger thannecessary. This is because the additional parameters of a larger filtercould adjust themselves to particular features of the specificrealization of the noise, i.e. the phenomenon sometimes referred to asoverfitting. To avoid this, a penalty factor α^(m) is introducedaccording to the Minimum Description Length Principle (MDL) (see e.g. R.Johansson, “System Modeling and Identification”, Prentice Hall, 1993).The penalty factor penalizes large equalizer spans m, and thereforesuppresses the effect of overfitting. In a preferred embodiment, thefactor α is determined by the length n of the training sequenceα=n^(1/n). Hence, in the example of a 16-symbol training sequenceα=1.189. It is noted, however, that alternatively other functionspenalizing large window spans may be used.

The optimization of eqn. (1) is performed both for p and m, where m isvaried in an interval between the upper and lower bounds m_(u) andm_(l), respectively, as will be described in greater detail below.

Still referring to FIG. 6, the optimization loop thus comprises thefollowing steps:

Step 602: Select a pair of values (p,m) within the intervals indicatedin eqn. (1).

Step 603: Estimate the transmission channel ĥ_(p,m) for the selectedvalues of p and m based on the stored training sequence t (608). When anLSE approach is used for joint synchronization and equalizer windowsizing, for a hypothetical sync position p and an equalizer window sizem, channel estimation can be computed ash=Φ ⁻¹ t*r=( 1/16)t*r.

With the exception of the constant factor, it can be further expressedin an explicit convolution form,

$\begin{matrix}{{{{{\hat{h}}_{p,m}(k)} = {\sum\limits_{i}{{t( {m + i - k} )} \cdot {r( {p + m - i} )}}}},{0 \leq p \leq w}}{0 \leq k \leq m}} & (4)\end{matrix}$

This can be considered as a FIR-style computation. For the next tap withk+1, a recurrent relation can be established:ĥ _(p,m)(k+1)=ĥ_(p+1,m)(k)+t(m−1−k)·r(p+m)−t(m+(n-1)−k)·r(p+m+n).   (5)

By using this two-dimensional (sync-point tap-position) recursiverelation in an IIR-style computation, a new tap can be calculated usingonly 4 real MAC operations (since the training sequences are real).

Step 604: Calculate the generalized error ε²(p,m). It is noted that, for16-symbol GSM training sequences and with m<8, the generalized errorε²(p,m) may be expressed asε²(p,m)=α^(m)(|r| ²−16ĥ _(p,m)|²), ε²>0.

Hence, in this case, the error measure ε²(p,m) may be efficientlycalculated as the difference of the received signal power |r|² and thescaled power of the estimated channel taps 16·|ĥ_(p,m)|², i.e. withoutthe need for calculating the actual noise. It is noted, that theconstraint ε²>0 is explicitly enforced, since the expression|r|²−16|ĥ_(p,m)|² may become negative at incorrect synchronizationpositions. Hence, when 16|ĥ_(p,m)|²≧|r|² no further calculation isnecessary and the hypothetical synchronization position is rejectedimmediately, since the constraint is not met.

Step 605: Repeat the above steps until a suitable minimum is found. Inone embodiment, the error is calculated for all possible pairs (p,m)within the above intervals, and the minimum of all calculated values isdetermined as the optimal set of values (p,m)_(opt).

When the optimal set of values (p,m)_(opt) is determined, in step 606the aperture for the span optimization of the subsequent burst, i.e. theupper and lower bounds m_(u) and m_(l), is determined and stored (607)for use in the subsequent optimization. According to this embodiment, anadaptive aperture is achieved by use of a simple auto regressive (AR)filter with one state m_(s) that is updated at each burst:m _(s)(t)=a·m _(s)(t−1)+b·m(t),where m(t) is the current equalizer span determined by the aboveoptimization. Hence, the state m_(s)(t) corresponds to a weighted meanof the previously determined equalizer spans, where the spans determinedfor the most recent bursts are weighted strongest. A suitable initialvalue is assumed, e.g. m_(s)(t=1)=m(t−1)=(m_(min)+m_(max))/2. Therelative weights are determined by the parameters a and b. Preferably aand b are selected in the interval [0,1], preferably such that a>b, e.g.a∈=[O.8,0.9] and b∈[0.1,0.2], for example a=0.875 and b=0.125. Largervalues of a reduce the relative influence of the most recent changes andvice versa, i.e. preferably the

1. A method of determining a DC offset in a communications signalreceived via a communications channel, the communications signalcomprising a sequence of training symbols; the method comprising;providing a channel estimate of the communications channel based on saidsequence of training symbols; determining, based on the channelestimate, an estimate of a noise contribution introduced by thecommunications channel; and determining an estimate of the DC offsetfrom the determined estimate of the noise contribution, wherein the stepof determining an estimate of the DC offset from the determined estimateof the noise contribution comprises calculating an inner product of arotation trend vector and an estimated noise vector representing thedetermined estimate of the noise contribution.
 2. An arrangement fordetermining a DC offset in a communications signal received via acommunications channel, the communications signal comprising a sequenceof training symbols; the arrangement comprising; processing meansadapted to provide a channel estimate of the communications channelbased on said sequence of training symbols; processing means adapted todetermine, based on the channel estimate, an estimate of a noisecontribution introduced by the communications channel; and processingmeans adapted to determine an estimate of the DC offset from thedetermined estimate of the noise contribution, wherein the processingmeans adapted to determine an estimate of the DC offset from thedetermined estimate of the noise contribution calculates an innerproduct of a rotation trend vector and an estimated noise vectorrepresenting the determined estimate of the noise contribution.
 3. Thearrangement of claim 2, implemented in a receiver for receiving acommunications signal via a transmission channel.